A More Technical Take on Logits

Mathematically, the logit is the inverse of the standard logistic function.

sigma(x) = 1 / (1+ exp(-x)) 

Note that the standard logistic function has only positive signs in it, the only hint of anything negative is the presence of the negative exponentation.

Hence logit is equal to

sigma^(-1)(p) = ln (p/ (1-p)) for p in (0,1).

Due to this, we sometimes call logit as log-odds, since it is the logarithm of the odds function p/(1-p) where p is probability. 

However, this definition is like getting the answer to something where you don't know the question.